The Corona theorem for Denjoy domains
type: Item
instance of: scholarly article
title: The Corona theorem for Denjoy domains
zbMATH Open document ID: 0578.30043
DOI: 10.1007/BF02392536
author: John B. Garnett
author: Peter Jones
published in: Acta Mathematica
publication date: 1985-01-01T00:00:00Z
review text: The authors prove the famous corona theorem for the space of bounded analytic functions on any Denjoy domain, i.e. a connected open subset \(\Omega\) of the extended complex plane \({\mathcal C}^*\) such that the complement \({\mathcal C}^*\setminus \Omega\) is a subset of the real axis. The proof utilizes the symmetry of the Denjoy domain and the relations between length, harmonic measure, relative to the upper half plane, and analytic capacity of linear sets.
Mathematics Subject Classification ID: 30H05
Mathematics Subject Classification ID: 46J15
Mathematics Subject Classification ID: 46J20
zbMATH DE Number: 3925227
zbMATH Keywords: corona theorem
zbMATH Keywords: space of bounded analytic functions
zbMATH Keywords: Denjoy domain
zbMATH Keywords: harmonic measure
zbMATH Keywords: analytic capacity
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02392536
OpenAlex ID: W2024457796
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description: scientific article; zbMATH DE number 3925227